摘要:
本文研究了在数学期望为零的高斯过程输入情况下,h(lx)具有h(k+p)(lx)=lph(k)(lx)(其中:h(k)(lx)=(k)h(lx)/xk,l为某个实数)性质的输出相关函数。 文中利用上述性质,由Price定理导出一常微分方程。将求非线性系统输出相关函数的问题,变成解常微分方程的问题。 所得结果表明:这类非线性系统的输出相关函数具有相同的形式。不同的h(lx)仅影响其系数。 在此基础上,文中将一般非线性系统的特性f(x)用具有上述性质的函数族来表示,然后直接引用文中前面所得的结果,非常简便地得出了一般非线性系统的输出相关函数的计算公式。
Abstract:
In this paper, the output correlation function of nonlinear systems of zero memory with the property of h(lx) characterized by h(k+p)(lx)=lph(k)(lx) (Where h(k)(lx)=(k)h(lx)/xk,l is a real number) is treated, in case of the gaussian process input with zeromathematical expectation.Based on the above characteristics, an ordinary differential equation is derived from Price theorem. Thus a problem of solving the output correlation function of nonlinear system is turned into a problem of solving an ordinary differential equation. The result show that the output correlation functions of nonlinear system of this kind are of the same form. Different h(lx)'s only exert their influences upon coefficients. From the above condition, the characteristic f(x) of the conventional nonlinear system may be expressed in a family of functions which has the performance as mentioned above. by using the results directly, it is easy to obtain a calculating equation concerning the output correlation function of the conventional nonlinear system.
下载:
